Estimation and Prediction for Exponentiated Family of Distributions Based on Records

Asgharzadeh, A.; Fallah, A.

doi:10.1080/03610920903350564

Cited by 18 publications

(5 citation statements)

References 20 publications

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“…To choose a joint prior distribution for ( , ) that incorporate uncertainty about both unknown parameters, we adopt the method proposed by Soland [27]. This method is also used by several researchers (see Asgharzadeh and Fallah [28]).…”

Section: Bayesian Estimationmentioning

confidence: 99%

Statistical Inference for Topp–Leone-generated Family of Distributions Based on Records

Arshad¹,

Azhad²

2019

JSTA

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In this paper, we consider a general family of distributions generated by Topp-Leone distribution (known as TL family of distributions) proposed by Rezaei et al. [1]. We consider the problem of estimation of the shape parameter, scale parameter, and reliability function based on record data from TL family of distributions. We derive the maximum likelihood estimator (MLE) for shape parameter, scale parameter, and reliability function. We have also obtained UMVUE (uniformly minimum-variance unbiased estimator) for reliability function when scale parameter is known. A Bayesian study is carried out under symmetric and asymmetric loss functions in order to find the Bayes estimators for unknown parameters and reliability function. Further, we have predicted future record values using Bayesian approach. A numerical comparison of various estimators is also reported.

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Section: Bayesian Estimationmentioning

confidence: 99%

Statistical Inference for Topp–Leone-generated Family of Distributions Based on Records

Arshad¹,

Azhad²

2019

JSTA

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“…Many authors studied record values and the associated statistics such as [1][2][3][4][5][6]. Furthermore, there are several studies which discussed some inferential methods based on record values for the Rayleigh [7,8], Weibull [9], inverse Weibull [10,11], exponentiated Family [12,13], Lomax [14,15], power Lindley model [16], exponentiated Weibull [17,18], and normal distribution [19].…”

Section: Introductionmentioning

confidence: 99%

Bayesian Estimations under the Weighted LINEX Loss Function Based on Upper Record Values

Al-Duais

2021

Complexity

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The essential objective of this research is to develop a linear exponential (LINEX) loss function to estimate the parameters and reliability function of the Weibull distribution (WD) based on upper record values when both shape and scale parameters are unknown. We perform this by merging a weight into LINEX to produce a new loss function called the weighted linear exponential (WLINEX) loss function. Then, we utilized WLINEX to derive the parameters and reliability function of the WD. Next, we compared the performance of the proposed method (WLINEX) in this work with Bayesian estimation using the LINEX loss function, Bayesian estimation using the squared-error (SEL) loss function, and maximum likelihood estimation (MLE). The evaluation depended on the difference between the estimated parameters and the parameters of completed data. The results revealed that the proposed method is the best for estimating parameters and has good performance for estimating reliability.

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“…Since then, such ordered data has been studied extensively in the literature. The problem of making inference based on record observations from a particular distribution has received attention of many researchers, and for literature on this topic one may refer to Soliman, Abd Ellah, and Sultan (2006) for the Weibull distribution, Asgharzadeh and Fallah (2011) for the exponentiated family of distributions, Dey, Dey, Salehi, and Ahmadi (2013) for the generalized exponential distribution, Kumar, Kumar, Saran, and Jain (2017) for the Kumaraswamy-Burr III distribution, Asgharzadeh, Fallah, Raqab, and Valiollahi (2018) for the Lindley distribution, Raqab, Bdair, and Al-Aboud (2018) for the two-parameter bathtubshaped distribution, and Pak and Dey (2019) for the power Lindley distribution.…”

Section: Introductionmentioning

confidence: 99%

Estimation and Prediction for the Power-Exponential Hazard Rate Distribution Based on Record Data

Tarvirdizade

Nematollahi

2019

American Journal of Mathematical and Management Sciences

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The problems of classical and Bayesian estimation of the parameters of the power-exponential hazard rate distribution (P-EHRD) based on record values and the prediction of future record values are considered. The parameters of P-EHRD are estimated by the maximum likelihood and the least squares methods, and the Bayes estimates are obtained by the Metropolis-Hastings method under the squared error loss and LINEX loss functions. Also, an asymptotic confidence interval, two bootstrap confidence intervals and the highest posterior density (HPD) credible interval for the unknown parameters are constructed. The problem of predicting the future record values from the P-EHRD based on the past record values is considered using the maximum likelihood and Bayesian approaches. To investigate and compare the performance of the different proposed methods, a Monte Carlo simulation study is conducted. Finally, an example is presented to illustrate the estimation and prediction procedures.

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Estimation and Prediction for Exponentiated Family of Distributions Based on Records

Cited by 18 publications

References 20 publications

Statistical Inference for Topp–Leone-generated Family of Distributions Based on Records

Statistical Inference for Topp–Leone-generated Family of Distributions Based on Records

Bayesian Estimations under the Weighted LINEX Loss Function Based on Upper Record Values

Estimation and Prediction for the Power-Exponential Hazard Rate Distribution Based on Record Data

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